Beijing's 2008 Olympic swimming stadium looks like a artifact from a dream: a giant box of glowing blue bubbles in which 17,000 people are concealed. Once you recover from the shock of seeing it, you start to wonder how anyone could possibly work out how to build it.
At first sight, the building looks like a surreal box of gigantic luminous blue bubbles. On closer inspection, it still looks like a surreal box of gigantic luminous blue bubbles, but it becomes apparent that those bubbles are made from a hugely complex network of steel bars sandwiched between translucent membranes of ETFE. And you can just about imagine how somebody could smoke a pipe or two of opium and dream it up – but how on earth did they design and build it?

Welcome to The Swimming Cube, one of the principal venues for the 2008 Beijing Olympic Games, designed and built by a consortium that includes Australian architect PTW, Arup and the China State Construction and Engineering Corporation. As you will have guessed, this structure houses the pools for the Olympic swimming and diving competitions, along with seating and facilities for 17,000 spectators.

This design of the cube was arrived at as the ideal solution to a number simultaneous problems. The most obvious was need to complement its neighbour, Herzog and de Muron's spectacular main stadium. That has an exposed bird's nest structure, which suggested that the swimming pool should follow suit. However, an exposed structure is difficult with to pull of with a swimming pool because it has to be enclosed to keep in the heat, and the steel structure has to be isolated from the corrosive atmosphere found in pools. And, because Beijing is in a seismic zone, the structure had to be earthquake proof. As if that were not enough, the team had less than a month to produce a worked-up design and submit it to for the competition.

The first part of the design was easy because there was little room to fit everything on the tight site. "We made a snap decision to go to a box as this allowed up to get everything on the site," says Tristram Carfrae, Arup's team leader on the project. "The next question was: 'How do we do this?'"

The first solution the team came up with was simple: structural steel tubes running vertically in the walls, and horizontally across the roof of a 185 m2 box. The problem was "how were we going to do the corners", says Carfrae. "We asked ourselves what 3D structure could go around corners."

The solution came by pure chance, when he spotted a structure similar to the tessellating bubbles produced by bubble-bath. "We saw a picture of an organic structure and thought: what is the geometry of that?" This bubble-like structure offered many advantages: it did not look strange at the corners of the building; it looked organic but was repeatable and therefore buildable; and it could easily be made to resist earthquakes.

When Carfrae started to research the interlinked bubble structure he found he was in a 100 year old mathematical minefield. Although this type of structure is so spatially efficient that it is a standard design for mineral crystals and biological cells, it is difficult to understand, let alone turn into a massive building (see "The physics of foam" on the next page). It took a week of intensive work before Carfrae felt he could present this his structural solution to the rest of the team.

When he did, the rest of the team quickly bought into his idea and now work concentrated on turning an obscure mathematical theory into a workable structure capable of resisting serious earthquakes. "We took this cellular structure and carved out the structure of our building," explains Carfrae. This was only the start of the process. "There were still lots of questions: how big the bubbles should be? What looks good? What works structurally?"

Arup then tried to draw the whole thing up in a CAD program. "It blew up every computer in our office," laughs Carfrae. Arup had to write its own computer program to carry out the structural analysis. According to Carfrae, simply adding a doorway meant that the whole structure had to change to compensate.

The final stage in the design was physically to model the structure. To do this, Arup used a technique called rapid prototyping; this is a machine that produces a real model from specially prepared CAD drawings. However, the team had to rely on Chinese craftsmanship. "We couldn't draw all the bubbles in time for the rapid prototyping machine, so we sent the simple 2D drawings to China and they built a model faster than the machine," says Carfrae.

Arup put the mathematical model into a CAD program. It blew up every computer in its office

The final result looks highly impressive.

The wall cavity is 3.5 m wide and the cavity forming the roof is 7 m deep. Although there are only two basic types of bubble in the structure, the way they are sliced through at the building's edges makes it appear as if there are 23 differently sized bubbles, which Carfrae says gives it an organic quality (see below).

All this hard work won the consortium the design competition. However, building the Water Cube will not be easy. The theoretical structural solution is elegant but structural realities are complicated. The structure is made up of a series of steel tubes welded to round steel nodes; these vary according to the loads acting upon them, which means there is a huge variety of steel tube and node sizes. There are 24,000 steel members and 12,000 nodes in total.

"There is architectural sophistication from the different tube sizes, this gives elegance to the structure, as the tubes are big where the forces are big, and smaller where the forces are less," says Carfrae. The steel tubes are also beefed up to resist potential earthquakes; indeed, Carfrae says the structure of the building is so strong it could be stood up on its end and retain its shape.

In addition to the aesthetic impact, the building envelope also helps to heat the space inside. Originally, the team hoped solar energy would have provided most of the energy needed for the building and pool, but budget constraints meant that the expensive solar shading and heat recovery systems had to be dropped. Even so, 20% of the solar energy falling on the greenhouse-like building is captured, and according to Carfrae this is equivalent to covering the entire roof in photovoltaic panels.

The physics of foam

What is the best way to tightly pack equally sized bubbles together without any gaps in between them? Carfrae found that this problem has been exercising minds for more than 100 years; the 19th-century physicist Lord Kelvin had tried to resolve the problem of how to fill a 3D space with equally sized volumes with the smallest amount of surface area between them. Kelvin’s answer was a 14-sided shape with its faces consisting of eight hexagons and six squares. Other mathematicians have tried to better this ever since.

Carfrae discovered that two Irish professors, Denis Weaire and Robert Phelan of Trinity College Dublin, had come up a better way of packing bubbles together in 1993. Two different 3D shapes of the same volume are needed for this solution. The first is a 12-sided shape called a dodecahedron. Its faces consist of equally sized pentagons. The second shape goes by the name of a tetrakaidecahedron. Its 14 sides consist of two hexagons and 12 pentagons. These two shapes are the basis of the Water Cube’s structure.

To make the bubble sizes appear more varied the arrangement of two 3D shapes has been rotated by 60°. If the bubbles were arranged in rows parallel to the surface, their size would appear repetitive where they are sliced through to form the edge of the building. Angling the bubbles at 60° gives greater variation in bubble size at the surface because the bubbles are sliced at different points.